snap to edge/vertex when scaling?
What you may do is to enable the Snapping Tool, change the snapping type to Vertex, then scale your object along the X axis (S,X) until it snaps to the other object. Then change the Y and Z  parameters of Scale in Transform panel to the same as X has (hover the cursor over the X value window, hold LMB and drag it down to copy the X value to other windows).


Before scaling an object make sure you snapped your 3D Cursor to its origin point (select an object in Object Mode, then press Shift+S-->Cursor to Selected). Also the pivot center type has to be set to 3D Cursor.